A fuse or fuse wire performs exact the same function as a circuit breaker.
their job is to monitor the current (power)** and to turn off the supply to that circuit if their is an overload.
the fuse works by having a thin piece of wire that is designed warm up when current flows through it. The material and thickness of the wire is designed so that if more current flows through it than the rated capacity then the wire melts and breaks, disconnecting the power until the fuse is replaced.
it is important to replace the wire with the correctly rated fuse wire.
a circuit breake does a similar thing, a small section of wire inside is designed to warm up and expand when current flows. Again this is sized according to the rated capacity of the circuit breaker. If too much current flows, the wire expands enough to operate a trigger mechanism that allows a spring to operate the circuit breaker “switch” and this disconnects the power until it is turned back on.
their is also a secondary trigger that is operated if a very large current is quickly detected (like a short circuit ) this is similar in operation to an electro magnet and can also trip the switch off.
in general, circuit breakers are more sensitive and faster operating than traditional fuse wire (in a domestic setting)
fuses are not inherently more dangerous than circuit breakers and in certain circumstances they are the better option (although generaly not in domestic)
if the safety switch that is installed is their term for an RCD “Residual Current Device” aka GFCI then this should detect faults to ground that are too small for the fuse to notice.
in short, their is probably nothing to worry about but if you have concerns about the installation then perhaps employ a registered electrician to report on the condition of the installation and advise you of any repairs or upgrades that are needed or recommended.
** current is not the same as power, however the relationship between them is directly linked and an increase in one will cause a comparable increase of the other.
i.e. If you double the power then you will double the current.